NASA Technical Reports Server (NTRS) 19980007201: Aeroelastic Analysis of Modern Complex Wings

8 Pages·0.52 MB·English

by  NASA Technical Reports Server (NTRS)

dccF-,Jc97
l_l;_/ d_ -- qb' _ I12621
AEROELASTIC ANALYSIS OF MODERN COMPLEX WINGS
Rakesh K. Kapania" and Manoj K. Bhardwaj** "_¢/"_ _
Virginia Polytechnic Institute and State University _/lf _ _:_ _
Biacksburg, VA 24060-0203
Eric Reichenbach t
McDonnell Douglas Aerospace
St. Louis, Missouri 63166
Guru P. Guruswamy ¢
Computational Aerosciences Branch
NASA Ames Research Center, Moffett Field, CA 94035-1000
Abs_act which introduce acertain level of complexity. This
complexity isrelated to the level of fluid and/or
A process is presented by which aeroelastic analysis is structural model used. Recently the Virginia Tech
performed by using an advanced computational fluid Multidisciplinary Analysis and Design (MAD) Center
dynamics (CFD) code coupled with an advanced Advisory Board met to discuss the needs of industry in
computational structural dynamics (CSD) code. The performing multidisciplinary analysis. There was
process is demonstrated on an F/A- 18Stabilator using expressed a strong need for a robust interface process
NASTD (an in-house McDonnell Douglas Aerospace that will allow a coupling of two independent codes,
East CFD code) coupled with NASTRAN. The process specifically a fluids analysis code and a structural
is also demonstrated on an aeroelastic research wing analysis code, to perform aeroelastic analysis. And
(ARW-2) using ENSAERO (an in-house NASA Ames with advanced subsonic transports entering into the
Research Center CFD code) coupled with a finite transonic regime and fighter aircraft being limited by
element wing-box structures code. Good results have aeroelastic phenomena, it is becoming increasingly
been obtained for the F/A-18 Stabilator while results important to perform static and dynamic aeroelastic
for the ARW-2 supercritical wing are still being analysis using highly accurate fluid and structural
obtained. models.
Introduction Work has been done coupling the fluid and structural
domains to perform static aeroelastic analysis. Euler
Aeroelastic analysis requires solutions of both the fluid flow equations coupled with finite element wing-box
and structural equations together. Both uncoupled and structures using a simple interface procedure between
coupled methods exist in solving these non-linear the two domains is used to perform static aeroelastic
system of equations n. The less expensive uncoupled analysis as can be seen in ref. 2. Also, recently Euler
methods can only handle small perturbations with flow equations coupled with finite element wing-box
moderate non-linearity. Aeroelastic problems involve structures using better triangular elements than the
aerospace vehicles with large structural deformations study in reference 1are used to perform static
and highly non-linear characteristics, therefore fully aeroelastic analysis exploiting parallel computers (ref.
coupled methods are needed to solve these aeroelastic 3). Again, the interface procedure was a simple one.
problems accurately. Other methods involving the coupling of the fluid and
structural domains can also be seen in ref. 4.
Fully coupled methods require interface procedures
In this paper, a process is presented by which static
aeroelastic analysis is performed using highly detailed
*Professor, Aerospace and Ocean Engineering,
Associate Fellow AIAA computational fluid dynamics (CFD) and highly
detailed computational structural dynamics (CSD). The
*'Graduate Research Assistant, Aerospace and Ocean
process deals with the interfacing of two separate codes
Engineering, Student Member AIAA
in the CSD and CFD fields.
)Senior Project Engineer, Member AIAA
:Research Scientist, Associate Fellow AIAA
Copyright© 1996byKapaniaetal.PublishedbyAmerican
irtstituteofAeronauticsandAstronautics,Inc.withpermission.
1
American Institute of Aeronautics and Astronautics
Aeroelastic Coupling Procedure triangles, the largest vertex distance is measured for
each triangle, where vertex distance is the distance
The process by which static aeroelastic analysis isto be between the structural node and CFD point (i,k).
performed is broken down into the following steps: Finally, the triangle with the smallest largest vertex
distance is chosen. Now that the structural triangle is
I) Get CFD solution known, the area coordinates of the CFD point are used
2) Calculate pressures at CFD grid points on to distribute the force to the nodes of the structural
aerodynamic surface triangle. So for each CFD point (i,k), the necessary
3) Map pressures on CFD grid to forces on CSD weight factors and destination nodes are known in the
grid preprocessing stage as well as the direction of the
4) Obtain response of the structure application of the loads. As a side note, the 20 closest
5) Map displacements on CSD grid to points can be changed to 25 closest points depending
displacements on aerodynamic surface of the CFD on the density of the structural grid.
grid
6) Deform entire CFD grid Now that the forces on the CSD grid are known, the
7) Repeat steps until convergence criteria is met structural response of the system is calculated. This is
done by solving the following system of equations
The above steps will sometimes be referred to later as [K]{u,}={fs}. This can be done easily by any structural
one cycle. analysis tool to obtain the displacements, {us}, on the
CSD grid.
When obtaining the CFD solution, it need not be
converged completely in the first few cycles if starting Once the structural response, {us}, is known, the
from free stream boundary conditions, since the displacements, {u,}, on the aerodynamic portion of the
convergence of the aeroelastic process is usually CFD grid need to be calculated. This is done by using
oscillatory. But, to converge the aeroelastic process in a surface spline 5. The surface spline system of
fewer cycles, it is better to obtain the rigid steady state equations become [A]{c}={u_,l} where [A] is
solution before beginning the first cycle of the dependent on the coordinates of the spline points, {c} is
aeroelastic analysis process. This will help reduce the the vector of unknown coefficients of the surface spline
computational time if structural model will be changed equation, and {uspl}are the displacements at the spline
often. points. In the preprocessing stage, some of the
structural nodes are chosen as the spline points. Once
After the pressures on the aerodynamic surface of the the spline points are chosen, [A] is formed using the
CFD grid are calculated, they are mapped from the coordinates of the spline points. After the structural
CFD grid to forces on the CSD grid. This involves a response, {us}, is obtained, the spline point
preprocessed mapping. The mapping consists of the displacements, {usF0, are extracted, and {c} is
following information. For each CFD point (i,k) on the calculated. Now, the displacements on the
aerodynamic surface, the area on which the pressure aerodynamic surface portion of the CFD grid, {u,}, are
acts and unit normal iscalculated. Now, the magnitude calculated using the coordinates of the CFD grid points.
and direction of the force due to unit pressure are
known. The next step is to f'md a structural triangle that Now that {u,} are known, the next step is to deform the
surrounds the CFD point (i,k). This can be difficult due entire CFD volume grid. This is dependent on the fluid
to the irregular grids of some structural models. analysis tool. In this study, two separate codes for fluid
analysis are used. One of the codes, ENSAERO, has a
It is assumed that the structural grid is divided into an built in scheme to move the grid, once the surface grid
upper and lower surface structural grids with isdeformed. The other code used, NASTD, does not
overlapping points possibly occurring at the leading have ascheme to move the grid. So a simple grid
and trailing edges and also at the tip. To find the moving scheme isapplied to the case when NASTD is
structural triangle associated with the CFD grid point, used, which is dependent on the CFD grid of the
the 20 closest structural nodes are found using the aerodynamic surface. It simply uses the deflections
upper or lower surface structural grid depending on calculated, {u,}, and moves the aerodynamic surface
which surface the CFD point is located. Then all the same amount. The remaining grid is deformed in
possible triangles using the 20 points are formed. Next, the normal direction using a spacing function that
the triangles that do not contain the CFD point (i,k) as varies smoothly from 1to 0. This will be discussed
an interior point are eliminated. Then of the remaining more when describing the specific example used.
2
American Institute of Aeronautics and Astronautics
Firstt,he process is demonstrated by using Euler flow Next, the remaining grid is deformed. In this case, the i
equations in NASTD (an in-house McDonnell Douglas index varies circumferentially around the wing section,
Aerospace East CFD code) and an advanced structural j index varies in the normal direction, and k index
analysis tool, NASTRAN. The F/A- 18 Stabilator varies along the span. Once the surface deflections are
(horizontal tail) is used to demonstrate the process, and known, acosine spacing function is used to deform the
results have been acquired for this example. grid at each k=constant face. The spacing function is
dependent on the normal index j. The outer boundaries
Next, the process is demonstrated by using Euler flow of the grid do not move. This is done to take advantage
equations in ENSAERO6"7(an in-house NASA Ames of distributed computing capabilities in the future,
Research Center CFD code) and a finite element wing- where the CFD grid can be broken down into multiple
box structural model. A supercfitical wing s(ARW-2) zones. In this case the CFD grid is broken into two
is chosen to demonstrate the process. Results are being zones, but distributed computing was not used. ARer
obtained for this example. the grid is deformed, the cycle is repeated until some
convergence criteria is met. As anote, the number of
F/A- 18 Stabilator iterations for the convergence of the CFD solution
varied during each cycle. No exact number of
As mentioned earlier, the F/A-I 8 Stabilator ischosen to iterations were used for each cycle, but the difference
demonstrate the process using Euler flow equations as between the iterations per cycle was minimal.
used in NASTD at sea-level, one degree angle of
attack, Mach 0.95. The CFD grid of the F/A-18 ARW-2 Supercritical Wing
Stabilator, approximately 800,000 grid points, is shown
in figure 1. NASTRAN is used to analyze the structure. The next case involves the ARW-2 Supercritical Wing.
The stiffness matrix produced by NASTRAN is used to As mentioned earlier, Euler equations as demonstrated
get the displacements given the loads, therefore during by ENSAERO are used to obtain the CFD solution.
the aeroelastic analysis process, NASTRAN is not While structural analysis is done using a finite element
directly involved, since the stiffness matrix does not wing-box structures code. The finite element wing-box
change during the process The finite element model of model iscreated using axial bars in conjunction with
the F/A-18 Stabilator is shown in figure 2 which Allman's triangular element 9,which is a nine d.o.f.
consists of approximately 2000 nodes, 12000 d.o.f. So element with two in-plane translations and an in-plane
step 1involves getting the CFD solution. For this case, rotation at each node. The element can represent all
the rigid steady state solution is obtained before the constant strain states exactly, thus assuring convergence
aeroelastic analysis cycle begins. Once the CFD with consistent mesh refinement.
solution isobtained, the forces on the CSD grid are
calculated using the preprocessed mapping, The The solver for structural domain is adirect solver
mapping of the CFD points to the structural triangles as which employs aparallelized '° LDL tmethod. The
discussed before is graphically shown in figure 3. stiffness matrices are stored in a skyline fashion
reducing storage requirements. This is done so that the
Now that the forces on the CSD grid are known, power of parallel computing as it applies to aeroelastic
NASTRAN is used to obtain the structural response. analysis can be exploited in the very near future.
Next, the displacements at the spline points are
extracted. The spline points for this case are shown in The CFD grid of the ARW-2 supercritical wing is
figure 4. The reason for this choice can be seen when shown in figure 6, which consists of approximately
looking at figure 5, which isthe surface grid of the 400,000 grid points. The f'mite element wing-box
F/A-18 Stabilator. The surface grid includes the model is shown in figures 7and 8. Figure 7shows the
aerodynamic surface and the points extending beyond entire wing as it is discretized, while figure 8 shows the
the wing tip in the spanwise direction, and the points spars and ribs of the structure. The f'mite element
extending beyond the trailing edge in the chordwise model consists of approximately 400 nodes, 2400 d.o.f.
direction. The points not on the aerodynamic surface
are chosen so the displacements vary smoothly from the At_er the CFD solution of the ARW-2 supercritical
aerodynamic surface to the farfield. So, using the wing is obtained, the next step is to use the mapping to
preprocessed mapping the surface spline coefficients transfer the pressures on the CFD grid to forces on the
are solved, and the deflections on the CFD surface grid CSD grid. The mapping of the CFD grid points to the
are calculated. CSD grid is shown in figure 9. Once the forces on the
3
American Institute of Aeronautics and Astronautics
structure are known, the displacements are easily
solved by using the finite element wing-box code. The aeroelastic coupling process has been successfully
demonstrated using the F/A-18 Stabilator, while results
Once the displacements on the CSD grid, {u,} are for the ARW-2 supercritical wing are still being
known, the spline point displacements {u_m}are obtained. Itwas shown that the process, though
extracted. The spline points used for the ARW-2 somewhat problem dependent, is robust in coupling an
advanced CFD tool with an advanced CSD tool. The
supercritical wing are shown in figure 10. So the
surface spline system of equations is solved and the coupling is done before the aeroelastic process is begun
coefficients of the surface spline equation are known. by creating mappings which transfer pressures on the
Now the CFD surface grid is deformed using the CFD grid to forces on the CSD grid and the resulting
surface spline equation. displacements on the CSD grid back to the CFD grid to
deform it. The mappings require only the CFD surface
Once the CFD surface grid is deformed, the next step is grid and CSD grid point coordinates. In addition,
to deform the entire CFD volume grid. ENSAERO some user interface is required in choosing surface
already has an algebraic grid moving scheme which spline points from the CSD and CFD grids, thus
was used in this example (Ref. 4). Therefore, once the creating the problem dependency. Overall, the
CFD surface grid is deformed, the process of deforming aeroelastic coupling process has been successful.
the entire CFD volume grid is done using the CFD code
References
itself.
1. Guruswamy, G.P. and Yang, T.Y., "Aeroelastic
Time-Response Analysis of Thin Airfoils by Transonic
F/A- 18Stabilator Code LTRAN2", Computers andFluids, Vol. 9, No. 4,
Dec. 1980, pp. 409-425.
The convergence of the CFD solution is shown in
figure 11. The spikes coincide with each cycle. The 2. Macmurdy, D.E., Guruswamy, G.P., and Kapania,
convergence of the structural analysis isshown in R.K., "Static Aeroelastic Analysis of Wings Using
figure 12. Here the deflections at the trailing edge of Euler/Navier-Stokes Equations Coupled with Improved
the F/A-I 8 Stabilator are plotted after each cycle to Wing-Box Finite Element Structures ", AIAA Paper 94-
show the oscillatory convergence. Figure 13shows the 1587, April 1994.
convergence at the trailing edge tip. As can be seen,
good convergence is obtained, and the deformed and 3. Bhardwaj, M.K., Kapania, R.K., Byun, C., and
undeformed F/A- 18 Stabilator is shown in figure 14. Guruswamy, G.P., "Parallel Aeroelastic Computations
The pressure coefficient variation of the flexible versus By Using Coupled Euler Flow and Wing-Box
the rigid F/A-18 Stabilator is shown in figure 15, and Structural Models", AIAA Paper 95-1291, April 1995.
similarly the Mach number variation is shown in figure
16. As can be seen, the deflections are not large due to 4. Byun, C. and Guruswamy, G.P., "Wing-Body
the low angle of attack of the analysis. Aeroelasticity Using Finite-Difference Fluid/Finite
Element Structural Equations on Parallel Computers",
_,RW-2 Supercritical Wing AIAA Paper 94-1487, April 1994.
Results are still being obtained for the ARW-2 5. Harder, R.L. and Desmarais, R.N., "Interpolation
supercriticai wing. One of the problems isto develop Using Surface Splines", Journal of Aircraft, Vol. 9, No.
an equivalent isotropic wing that closely matched the 2, October 1971, pp. 189-191.
original ARW-2 supercritical wing which contains
composite skins. To validate the isotropic ARW-2 6. Guruswamy, G.P., "Coupled Finite-
wing, a tip load of 100 lb in the downward direction is Difference/Finite Element Approach for Wing-Body
applied, and the deflections compared. The deflections Aeroelasticity", AIAA Paper 92-4680, Sep. 1992.
along the front, rear, and auxiliary spars are compared
and are in good agreement. Figure 17shows the 7. Guruswamy, G.P. and Byun, C., "Fluid-Structural
displacements plotted along the span of the rear spar. Interactions Using Navier-Stokes Flow Equations
As can be seen, good agreement is obtained. Coupled with Shell Finite Element Structures", AIAA
Paper 93-3087, July 1993.
Conclusions
4
American Institute of Aeronautics and Astronautics
8,SanfordM,aynarCd.,SeidelD,avidA.,Eckstrom,
ClintonV.,andSpainC,harleVs.,"Geometricaanld
StructurPalropertieosfanAeroelastRicesearcWhing
(ARW-2)"N,ASATM4110A, pril1989.
9.AllmanD, .J.",ACompatibTleriangulaErlement
IncludinVgertexRotationfsorPlaneElasticity
Problems",
Computers and Structures, Vol. 19,No. 1-
2, 1984, pp. 1-8.
10. Farhat, C. and Wilson, E., "A Parallel Active
Column Equation Solver", Computers and Structures,
Vol. 28, No.2, 1988, pp. 289-304.
Figure 3- Mapping of CFD points to structural
triangles for F/A- !8 Stabilator
12_0
t 0 0 0
m 0 0 0
i °
0 0 0
0 0 0
i °
0 0 0
0 0 0
400 0 0 0
0 0 0
Figure 1- CFD grid of F/A- 18 Stabilator
Figure 4 - Spline points used for FIA- 18 Stabilator
Figure 2 - F/A-I 8 Stabilator Finite Element Model
Figure 5 - Entire surface grid of F/A-18 Stabilator
5
American Institute of Aeronautics and Astronautics
Figure 9- Mapping of CFD grid points to structural
Figure6-CFDgridofARW-2supercriticwailng
triangles for ARW-2 supercritical wing
_vv
2OO
0 0 0
150
0 0 0
| 0 0 0
c 0 D 0
I
0 0 0
0 0 0
GO 0 0 0
_000o 0 0 0
_00 O0 0 0 0
0_1 .... i ..... ,d .... i .... t .... i
Figure7-EntireARW-2supercriticwailngfinite GO 1® IGO 200 2GO 3OO
element model Sttwrata ¢,o0lar, m
Figure 10 - Spline points used for ARW-2 supercritical
.....----7_. _ wing
,111
41 ....
,.1 1l..,I
_ n _ i mmmal t
n
Figure 8- Spars and ribs of ARW-2 supercritical wing Figure 11- Convergence of CFD solution of F/A- 18
Stabilator
6
American Institute of Aeronautics and Astronautics
95..=
._95.0
--'V'- _=
E
!
_ _ja,s
= --0-- _
Figure 14 - Deformed and undeformed aerodynamic
surfaces of the F/A- 18 Stabilator
Streanm'_Coo_mie(in)
Figure 12- Convergence of structural analysis for the
F/A- 18 Stabilator
95.5
r,-
95.0
i
c,)
m
Q
g
,,,I .... I .... I .... I .... I_ll,l,,l,I Rigid
2 3 4 5 6 7 6
\
Figure 13- Convergence of the trailing edge tip of the
F/A- 18 Stabilator Figure 15 - Pressure coefficient variation of flexible
and rigid F/A- 18 Stabilator
7
American Institute of Aeronautics and Astronautics
Flexible
13 W L_ 7J
Rigid
Figure 16 - Mach number variation of flexible and
rigid F/A- 18 Stabilator
-05
-L0
e_
20 40 80 80 100
SpenwCisoeod_ef=)
Figure 17 - Comparison of rear spar displacements of
composite and isotropic ARW-2 supercritical wing
8
American Institute of Aeronautics and Astronautics